Problem: Brandon is 3 times as old as Vanessa. Twelve years ago, Brandon was 5 times as old as Vanessa. How old is Vanessa now?
Answer: We can use the given information to write down two equations that describe the ages of Brandon and Vanessa. Let Brandon's current age be $b$ and Vanessa's current age be $v$ The information in the first sentence can be expressed in the following equation: $b = 3v$ Twelve years ago, Brandon was $b - 12$ years old, and Vanessa was $v - 12$ years old. The information in the second sentence can be expressed in the following equation: $b - 12 = 5(v - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $v$ , it might be easiest to use our first equation for $b$ and substitute it into our second equation. Our first equation is: $b = 3v$ . Substituting this into our second equation, we get: $3v$ $-$ $12 = 5(v - 12)$ which combines the information about $v$ from both of our original equations. Simplifying the right side of this equation, we get: $3 v - 12 = 5 v - 60$ Solving for $v$ , we get: $2 v = 48.$ $v = 24$.